What is/are the same for $O_2$ and $NH_3$ in gaseous state?

Which of the following graphs represents the variation of $\beta = -(dV/dP)$ with pressure $P$ for an ideal gas kept at a constant temperature?

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Statement $I$: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U = nC_v(T_f - T_i) = \frac{nR}{\gamma - 1}(T_f - T_i)$, where $\gamma = C_p/C_v, T_i = $ initial temperature, $T_f = $ final temperature. Statement $II$: Relation between degree of freedom $f$ and $\gamma(= C_p/C_v)$ is $\gamma = 1 + \frac{2}{f}$. Choose the correct answer from the options given below.

Match Column $- I$ and Column $- II$ and choose the correct match from the given choices.

Column $- I$	Column $- II$
$(A)$ Root mean square speed of gas molecules	$(P)$ $\frac{1}{3} n m \bar{v}^{2}$
$(B)$ Pressure exerted by ideal gas	$(Q)$ $\sqrt{\frac{3 RT}{M}}$
$(C)$ Average kinetic energy of a molecule	$(R)$ $\frac{5}{2} RT$
$(D)$ Total internal energy of $1$ mole of a diatomic gas	$(S)$ $\frac{3}{2} k_{B} T$

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: The internal energy of a perfect gas is entirely kinetic and depends only on the absolute temperature of the gas and not on its pressure or volume.
Statement-$2$: $A$ perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat,the temperature rise of the gas at constant pressure is lower than that at constant volume.

$A$ box contains $N$ molecules of a perfect gas at temperature ${T_1}$ and pressure ${P_1}$. The number of molecules in the box is doubled while keeping the total kinetic energy of the gas the same as before. If the new pressure is ${P_2}$ and temperature is ${T_2}$,then: